[Charlie Hough]

Playing as a DH definitely saves some of a player's fatigue, but it's not the same as 100% resting. They're still being used, so they could eventually need to be rested.

As for a maximum number of innings, do you mean a maximum limit that the game imposes before a pitcher can continue to pitch in a game? Or do you mean a limit on their season innings? In either case, there is no maximum, but pitchers will get fatigued once they throw enough pitches, or they will have increased injury risk if they're overworked during a season. Their threshold depends on what era you're playing in, your league's pitcher fatigue settings, and individual pitcher fatigue ratings.

In individual games, you can pitch them into exhaustion and keep using them, although I would not recommend that. I usually replace pitchers once they start showing fatigue in a game, or shortly thereafter. Their performance will often suffer if you don't. Over a full season, it certainly seems that the risk of late-season injury increases if a pitcher has been worked really hard all season, so I recommend paying attention to pitch counts and taking opportunities to ease some of the workload, particularly toward the end of the season. For example, if I'm managing a team that has secured a playoff spot or is out of the playoffs, then I'll try to ease up on my starters and manage their innings more carefully. Earlier in the season, if we're winning a blowout game, then I might let the bullpen finish out the final few innings. But a lot depends on the pitch count.